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Symmetric matrix. More...
#include <MatrixBase.h>
Public Types | |
typedef VectorGeneral< Treal, typename Tmatrix::VectorType > | VectorType |
typedef Treal | real |
Public Member Functions | |
MatrixSymmetric () | |
Default constructor More... | |
MatrixSymmetric (const MatrixSymmetric< Treal, Tmatrix > &symm) | |
Copy constructor More... | |
MatrixSymmetric (const XY< Treal, MatrixSymmetric< Treal, Tmatrix > > &sm) | |
MatrixSymmetric (const MatrixGeneral< Treal, Tmatrix > &matr) | |
'Copy from normal matrix' - constructor More... | |
void | assignFromFull (std::vector< Treal > const &fullMat) |
void | assignFromFull (std::vector< Treal > const &fullMat, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
void | fullMatrix (std::vector< Treal > &fullMat) const |
Save matrix as full matrix. More... | |
void | fullMatrix (std::vector< Treal > &fullMat, std::vector< int > const &rowInversePermutation, std::vector< int > const &colInversePermutation) const |
Save matrix as full matrix. More... | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values) |
Assign from sparse matrix given by three vectors. More... | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, SizesAndBlocks const &newRows, SizesAndBlocks const &newCols) |
Assign from sparse matrix given by three vectors. More... | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. More... | |
void | assign_from_sparse (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, SizesAndBlocks const &newRows, SizesAndBlocks const &newCols, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking sizes and blocks arguments. More... | |
void | add_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values) |
Add given set of values to the matrix. More... | |
void | add_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > const &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. More... | |
void | get_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > &values) const |
Get values given by row and column index lists. More... | |
void | get_values (std::vector< int > const &rowind, std::vector< int > const &colind, std::vector< Treal > &values, std::vector< int > const &rowPermutation, std::vector< int > const &colPermutation) const |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. More... | |
void | get_all_values (std::vector< int > &rowind, std::vector< int > &colind, std::vector< Treal > &values) const |
Get all values and corresponding row and column index lists, in matrix. More... | |
void | get_all_values (std::vector< int > &rowind, std::vector< int > &colind, std::vector< Treal > &values, std::vector< int > const &rowInversePermutation, std::vector< int > const &colInversePermutation) const |
Same as above, except taking two additional arguments specifying the permutation of rows and columns. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const MatrixSymmetric< Treal, Tmatrix > &symm) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const MatrixGeneral< Treal, Tmatrix > &matr) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (int const k) |
Treal | frob () const |
Treal | mixed_norm (Treal const requestedAccuracy, int maxIter=-1) const |
Treal | eucl (Treal const requestedAccuracy, int maxIter=-1) const |
void | quickEuclBounds (Treal &euclLowerBound, Treal &euclUpperBound) const |
Treal | thresh (Treal const threshold, normType const norm) |
Does thresholding so that the error in the chosen norm is below the given threshold. More... | |
Treal | frob_thresh (Treal const threshold) |
Does thresholding so that the error in the Frobenius norm is below the given threshold. More... | |
Treal | eucl_thresh (Treal const threshold, MatrixTriangular< Treal, Tmatrix > const *const Zptr=NULL) |
Treal | eucl_element_level_thresh (Treal const threshold) |
void | getSizesAndBlocksForFrobNormMat (SizesAndBlocks &rows_new, SizesAndBlocks &cols_new) const |
Treal | mixed_norm_thresh (Treal const threshold) |
void | simple_blockwise_frob_thresh (Treal const threshold) |
void | gershgorin (Treal &lmin, Treal &lmax) const |
size_t | nnz () const |
size_t | nvalues () const |
void | write_to_buffer (void *buffer, const int n_bytes) const |
void | read_from_buffer (void *buffer, const int n_bytes) |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B = alpha * A : A and B are symmetric. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZpUV< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > &sm2psm) |
C = alpha * A * A + beta * C : A and C are symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > &sm2) |
C = alpha * A * A : A and C are symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > &sm2) |
C += alpha * A * A : A and C are symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZpUV< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > &smmpsm) |
C = alpha * A * transpose(A) + beta * C : C is symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > &smm) |
C = alpha * A * transpose(A) : C is symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > &smm) |
C += alpha * A * transpose(A) : C is symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (const XYZ< MatrixTriangular< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, MatrixTriangular< Treal, Tmatrix > > &zaz) |
A = Z * A * transpose(Z) : Z is upper triangular and A is symmetric; A = transpose(Z) * A * Z : Z is upper triangular and A is symmetric. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XpY< MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > const &mpm) |
C = A + B : A, B, and C are symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator= (XmY< MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > const &mm) |
C = A - B : A, B, and C are symmetric More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (MatrixSymmetric< Treal, Tmatrix > const &A) |
B += A : A and B are symmetric. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator-= (MatrixSymmetric< Treal, Tmatrix > const &A) |
B -= A : A and B are symmetric. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator+= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B += alpha * A : A and B are symmetric. More... | |
MatrixSymmetric< Treal, Tmatrix > & | operator-= (XY< Treal, MatrixSymmetric< Treal, Tmatrix > > const &sm) |
B -= alpha * A : A and B are symmetric. More... | |
template<typename Top > | |
Treal | accumulateWith (Top &op) |
void | random () |
void | randomZeroStructure (Treal probabilityBeingZero) |
template<typename TRule > | |
void | setElementsByRule (TRule &rule) |
Uses rule depending on the row and column indexes to set matrix elements The Trule class should have the function "Treal = set(int row,int col)" which is used to set the elements. More... | |
void | transfer (MatrixSymmetric< Treal, Tmatrix > &dest) |
Transfer this matrix to dest, clearing previous content of dest if any. More... | |
template<typename Tvector > | |
void | matVecProd (Tvector &y, Tvector const &x) const |
std::string | obj_type_id () const |
Static Public Member Functions | |
static Interval< Treal > | diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, normType const norm, Treal const requestedAccuracy) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) More... | |
static Interval< Treal > | diffIfSmall (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, normType const norm, Treal const requestedAccuracy, Treal const maxAbsVal) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) based on the chosen norm. More... | |
static Treal | frob_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B) |
Returns the Frobenius norm of A - B ( || A - B ||_F ) More... | |
static Treal | eucl_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy, int maxIter=-1) |
Returns the Euclidean norm of A - B ( || A - B ||_2 ) More... | |
static Treal | mixed_diff (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy) |
Returns the 'mixed' norm of A - B ( || A - B ||_mixed ) More... | |
static Interval< Treal > | euclDiffIfSmall (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, Treal const requestedAccuracy, Treal const maxAbsVal, VectorType *const eVecPtr=0) |
Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ). More... | |
static Treal | trace_ab (const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B) |
static void | ssmmUpperTriangleOnly (const Treal alpha, const MatrixSymmetric< Treal, Tmatrix > &A, const MatrixSymmetric< Treal, Tmatrix > &B, const Treal beta, MatrixSymmetric< Treal, Tmatrix > &C) |
C = alpha * A * B + beta * C where A and B are symmetric and only the upper triangle of C is computed, C is enforced to be symmetric! More... | |
Protected Member Functions | |
void | writeToFileProt (std::ofstream &file) const |
void | readFromFileProt (std::ifstream &file) |
Static Protected Member Functions | |
static void | getPermutedAndSymmetrized (std::vector< int > const &rowind, std::vector< int > const &rowPermutation, std::vector< int > &newRowind, std::vector< int > const &colind, std::vector< int > const &colPermutation, std::vector< int > &newColind) |
This function permutes row and column indices according to the specified permutation and gives the indices as upper triangle in the new permutation. More... | |
Symmetric matrix.
This class belongs to the matrix API
The matrix is stored in the upper triangle.
Treal: Type for real numbers
Tmatrix: The matrix class
typedef Treal mat::MatrixSymmetric< Treal, Tmatrix >::real |
typedef VectorGeneral<Treal, typename Tmatrix::VectorType> mat::MatrixSymmetric< Treal, Tmatrix >::VectorType |
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Default constructor
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Copy constructor
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'Copy from normal matrix' - constructor
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Add given set of values to the matrix.
The values should be given in upper triangular storage.
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
References mat::MatrixSymmetric< Treal, Tmatrix >::getPermutedAndSymmetrized().
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Assign from sparse matrix given by three vectors.
The vectors contain row indices, column indices and values. The indices start at zero. The elements to be added must be given in upper triangluar storage. Information about sizes and blocks for rows as well as columns must also be given. Assumes that sizes and blocks are already set.
Referenced by mat::MatrixSymmetric< Treal, Tmatrix >::assign_from_sparse(), mat::MatrixSymmetric< Treal, Tmatrix >::assignFromFull(), main(), mainFun(), test1(), test2(), test3(), and test4().
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Assign from sparse matrix given by three vectors.
The vectors contain row indices, column indices and values. The indices start at zero. The elements to be added must be given in upper triangluar storage. Information about sizes and blocks for rows as well as columns must also be given.
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Same as above, except taking sizes and blocks arguments.
References mat::MatrixSymmetric< Treal, Tmatrix >::assign_from_sparse().
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
Also, assuming that sizes and blocks are already set.
References mat::MatrixSymmetric< Treal, Tmatrix >::getPermutedAndSymmetrized().
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Referenced by mainFun().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 )
References A, B, mat::euclNorm, mat::frobNorm, and template_blas_sqrt().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ) based on the chosen norm.
BUT, in the case of Euclidean norm, the norm is only computed with the requested accuracy if it is smaller than 'maxAbsVal'.
References A, B, mat::euclNorm, mat::frobNorm, and template_blas_sqrt().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl | ( | Treal const | requestedAccuracy, |
int | maxIter = -1 |
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References cols, mat::arn::LanczosLargestMagnitudeEig< Treal, Tmatrix, Tvector >::getLargestMagnitudeEig(), mat::VectorGeneral< Treal, Tvector >::rand(), mat::VectorGeneral< Treal, Tvector >::resetSizesAndBlocks(), and template_blas_fabs().
Referenced by mainFun(), and MatAccInvestigator< Treal, Tworker >::Scan().
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Returns the Euclidean norm of A - B ( || A - B ||_2 )
References A, B, mat::euclIfSmall(), mat::Interval< Treal >::midPoint(), and template_blas_sqrt().
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl_element_level_thresh | ( | Treal const | threshold | ) |
Treal mat::MatrixSymmetric< Treal, Tmatrix >::eucl_thresh | ( | Treal const | threshold, |
MatrixTriangular< Treal, Tmatrix > const *const | Zptr = NULL |
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References mat::EuclTruncationBase< Tmatrix, Treal >::run().
Referenced by mainFun().
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Returns interval containing the Euclidean norm of A - B ( || A - B ||_2 ).
BUT, the norm is only computed with the requested accuracy if it is smaller than 'maxAbsVal'. Otherwise, the Frobenius norm is used to get the bounds.
References A, B, mat::euclIfSmall(), mat::Interval< Treal >::length(), mat::Interval< Treal >::midPoint(), and template_blas_sqrt().
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Does thresholding so that the error in the Frobenius norm is below the given threshold.
Returns an upper bound of the introduced error. If no elements on the block diagonal are removed the return value is equal to the introduced error.
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Save matrix as full matrix.
Whole matrix is written in columnwise order. Both lower and upper triangle. NOTE that no permutation is used in this operation.
Referenced by mainFun().
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Save matrix as full matrix.
Whole matrix is written in columnwise order. Both lower and upper triangle. Permutation is used.
References mat::MatrixSymmetric< Treal, Tmatrix >::get_all_values().
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Referenced by mainFun().
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Get all values and corresponding row and column index lists, in matrix.
Only upper triangle values are returned.
References mat::MatrixSymmetric< Treal, Tmatrix >::nnz().
Referenced by mat::MatrixSymmetric< Treal, Tmatrix >::fullMatrix(), and mainFun().
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
Note, however, that this permutation is the inverse permutation compared to the permutations provided in the functions "assign_from_sparse", "add_values", and "get_values"
References mat::MatrixSymmetric< Treal, Tmatrix >::getPermutedAndSymmetrized().
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Get values given by row and column index lists.
Input arrays contain row and column indices. The wanted elements must be given in upper triangluar storage. The output array contains values for the given indices.
Referenced by mainFun().
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Same as above, except taking two additional arguments specifying the permutation of rows and columns.
References mat::MatrixSymmetric< Treal, Tmatrix >::getPermutedAndSymmetrized().
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This function permutes row and column indices according to the specified permutation and gives the indices as upper triangle in the new permutation.
References mat::MatrixBase< Treal, Tmatrix >::getPermutedIndexes().
Referenced by mat::MatrixSymmetric< Treal, Tmatrix >::add_values(), mat::MatrixSymmetric< Treal, Tmatrix >::assign_from_sparse(), mat::MatrixSymmetric< Treal, Tmatrix >::get_all_values(), and mat::MatrixSymmetric< Treal, Tmatrix >::get_values().
void mat::MatrixSymmetric< Treal, Tmatrix >::getSizesAndBlocksForFrobNormMat | ( | SizesAndBlocks & | rows_new, |
SizesAndBlocks & | cols_new | ||
) | const |
References cols, mat::SizesAndBlocks::getBlockSizeVector(), mat::SizesAndBlocks::getNTotalScalars(), and rows.
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Treal mat::MatrixSymmetric< Treal, Tmatrix >::mixed_norm | ( | Treal const | requestedAccuracy, |
int | maxIter = -1 |
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Treal mat::MatrixSymmetric< Treal, Tmatrix >::mixed_norm_thresh | ( | Treal const | threshold | ) |
References mat::EuclTruncationBase< Tmatrix, Treal >::run().
Referenced by mainFun().
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Referenced by mat::MatrixSymmetric< Treal, Tmatrix >::get_all_values(), and main().
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MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator+= | ( | const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > & | smm | ) |
C += alpha * A * transpose(A) : C is symmetric
References mat::syrk().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator+= | ( | const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > & | sm2 | ) |
C += alpha * A * A : A and C are symmetric
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B += A : A and B are symmetric.
References A.
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B += alpha * A : A and B are symmetric.
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B -= A : A and B are symmetric.
References A.
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B -= alpha * A : A and B are symmetric.
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References mat::MatrixBase< Treal, Tmatrix >::operator=().
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References mat::MatrixBase< Treal, Tmatrix >::operator=(), and mat::symm().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< MatrixTriangular< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, MatrixTriangular< Treal, Tmatrix > > & | zaz | ) |
A = Z * A * transpose(Z) : Z is upper triangular and A is symmetric; A = transpose(Z) * A * Z : Z is upper triangular and A is symmetric.
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix > > & | smm | ) |
C = alpha * A * transpose(A) : C is symmetric
References mat::syrk().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZ< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix > > & | sm2 | ) |
C = alpha * A * A : A and C are symmetric
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZpUV< Treal, MatrixGeneral< Treal, Tmatrix >, MatrixGeneral< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > & | smmpsm | ) |
C = alpha * A * transpose(A) + beta * C : C is symmetric
References mat::syrk().
MatrixSymmetric< Treal, Tmatrix > & mat::MatrixSymmetric< Treal, Tmatrix >::operator= | ( | const XYZpUV< Treal, MatrixSymmetric< Treal, Tmatrix >, MatrixSymmetric< Treal, Tmatrix >, Treal, MatrixSymmetric< Treal, Tmatrix > > & | sm2psm | ) |
C = alpha * A * A + beta * C : A and C are symmetric
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C = A - B : A, B, and C are symmetric
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C = A + B : A, B, and C are symmetric
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B = alpha * A : A and B are symmetric.
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References mat::MatrixSymmetric< Treal, Tmatrix >::frob(), and template_blas_sqrt().
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Referenced by mainFun().
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References mat::matrix_symm.
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References mat::matrix_symm.
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Uses rule depending on the row and column indexes to set matrix elements The Trule class should have the function "Treal = set(int row,int col)" which is used to set the elements.
Referenced by mainFun().
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Treal mat::MatrixSymmetric< Treal, Tmatrix >::thresh | ( | Treal const | threshold, |
normType const | norm | ||
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Does thresholding so that the error in the chosen norm is below the given threshold.
Returns the actual introduced error. In case of the Frobenius norm the return value may be an upper bound. In case of the Euclidean norm the return value is sometimes an upper bound as well but it can only happen if the whole matrix is removed.
References mat::euclNorm, mat::frobNorm, and mat::mixedNorm.
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Transfer this matrix to dest, clearing previous content of dest if any.
References mat::ValidPtr< Tobj >::swap().
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References mat::matrix_symm.
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References mat::matrix_symm.